Locating, characterizing and computing the stationary points of a function

A meth~ fi~r the hmalization, characterizadcm and ctnnputatitm of the stationary ptfints of a cxmtinutatsly differentiable real-valued fimction tff n variables is presented. It is based on the annbinatoriai topohgy concept of the degree of a mapping associated with an oriented polyhednm. The method consists of two principal steps: (i) Iocalizati, m (and am~putation if required) of a ~ationary point in an nMimensional polyhedron; (ii) characterizatkm of a stationary point as a minimum, maximmn or .saddle txfint. The method requires truly the .signs of gradient values to be currect and it can be successfiflly applied to pn~blems with impredse values.